Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cdtw)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=43/8, b>=a

For fixed z and a=43/8, b=45/8

http://functions.wolfram.com/07.23.03.cdtw.01

Input Form

Hypergeometric2F1[43/8, 45/8, -(1/2), -z] == (1/(244644 (1 + z)^(23/2))) ((-Sqrt[1 + z]) (-244644 - 17553207 z + 405386457 z^2 - 1329330758 z^3 + 1078766222 z^4 - 211688051 z^5 + 5730381 z^6) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-183483 - 64285466 z + 730047283 z^2 - 1798709964 z^3 + 1243780187 z^4 - 221910778 z^5 + 5730381 z^6) Sinh[(3 ArcSinh[Sqrt[z]])/4])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]